890 
; vast, the g,,’s must keep their values"). For the sake of 
simplicity changes of the entropy will not be considered, so that 
we have to do with adiabatic changes of the body only. HAMILTON’s 
function F must be regarded as a function of the @;;’s and of the 
of «x WL 
2? 
contravariant g”’’s 
5 =$ (aij, 9°). 
If the variation of § in a fixed point (w‚,w‚, z,, #‚) of the four- 
dimensional world is denoted by d *, and the variation in a point 
(E.E, EE) of the matter by AS, then we have 
it in _ Ow 
dj = AS — = — Gz; „ 
i Ow; 
OS Oda; 05 _ Og” 
Dn rn 
iy ET 
in Odjn OS, py Og? i Oa; 
Now the variation principle gives 
Ld x,y ,. 
=op fide: de, de, de, dz, = 
2 AP ‘\ x Outi Ò Og?” Ox 
II en Aint 2 5 = => ~— daj— = dw; )da.dx,da,dz,. 
in zo 3 j Oa; poe OG i Ov; i Ow; 
The dw,’s being independent of each other, we obtain by partial 
integration of the first term in brackets 
epe ME 0 ON OR Og”? 
— S— 2 ajax ee te 
5 One. Fi dai, Es an Og?” 02; 
If we put 
V = Da de ie 5 nah «~~ 28 
5 ” cs Oajn t ( ) 
where óf is 1 or O according as # and j are equal or not, it is 
easily proved that this expression (28) for Xl is identical with the 
first expression (23), if 4} and ® are connected by equation (25). 
If we put still 
EE a Yous En < ey ae ea ie eN (29) 
(comp. Este p. 1116) then we have according to (23a) 
$= eee a ee ee 
1) Einstein proceeds in the opposite way. He varies the gy’s, while the coordi- 
nates of the matter are kept constant. 
2) Acceording to (26) and (30) the right hand sid of (2) is therefore equal to — Ty. 
